Method for homomorphic encryption or decryption in consideration of spatial complexity

Abstract

An operation device is disclosed. The operation device includes a memory storing at least one instruction, and a processor executing the at least one instruction, wherein the processor is configured to, by executing the at least one instruction, perform decryption for a homomorphic encryption by using information for a secret key, and the secret key is expressed as a polynomial having a plurality of terms, and the information for the secret key includes information on degrees and coefficients of the plurality of respective terms.

What is claimed is: 
     
         1 . A method for processing a homomorphic encryption, the method comprising:
 receiving an input of a homomorphic encryption; and   outputting an approximate message for the input homomorphic encryption by using information for a secret key,   wherein the secret key is expressed as a polynomial having a plurality of terms, and   the information for the secret key includes information on degrees and coefficients of the plurality of respective terms.   
     
     
         2 . The method for processing a homomorphic encryption of  claim 1 ,
 wherein the secret key includes 64 terms, and   the coefficient information has a value of 1 or −1.   
     
     
         3 . The method for processing a homomorphic encryption of  claim 1 ,
 wherein the secret key is a polynomial calculated by using only a last decimal q 0  from a predetermined ring.   
     
     
         4 . The method for processing a homomorphic encryption of  claim 1 ,
 wherein the outputting an approximate message comprises:   performing inverse Number Theoretic Transformation (INTT) processing on the homomorphic encryption;   operating the iNTT-processed homomorphic encryption and the information for the secret key and calculating an approximate message in a polynomial form; and   decoding the calculated approximate message in a polynomial form and calculating the approximate message.   
     
     
         5 . The method for processing a homomorphic encryption of  claim 4 ,
 wherein the calculating an approximate message in a polynomial form comprises:   increasing an arrangement space of the iNTT-processed homomorphic encryption by two times, and repetitively operating coefficient information listed based on the degree information and the homomorphic encryption of which arrangement space was increased and shifting the coefficient information by stages from a low degree of the homomorphic encryption of which arrangement space was increased, and calculating the approximate message in a polynomial form.   
     
     
         6 . The method for processing a homomorphic encryption of  claim 4 ,
 wherein the calculating an approximate message in a polynomial form comprises:   dividing the arrangement space of the iNTT-processed homomorphic encryption into a plurality of sections, and performing an operation between the iNTT-processed homomorphic encryption and the coefficient information listed based on the degree information for the plurality of respective sections, and calculating the approximate message in a polynomial form.   
     
     
         7 . A method for processing a homomorphic encryption, the method comprising:
 receiving a homomorphic encryption;   converting the received homomorphic encryption into a polynomial;   modulus-operating the converted polynomial; and   converting the modulus-operated result into a homomorphic encryption,   wherein the converting into a polynomial comprises:   using a plurality of slot values inside the received homomorphic encryption as they are as a plurality of coefficient values of the polynomial.   
     
     
         8 . The method for processing a homomorphic encryption of  claim 7 ,
 wherein the converting into a homomorphic encryption comprises:   outputting a homomorphic encryption having the plurality of coefficient values of the polynomial which is the modulus-operated result as a plurality of slot values.   
     
     
         9 . The method for processing a homomorphic encryption of  claim 7 ,
 wherein the converting into a polynomial comprises:   based on a ratio of an approximate message inside the homomorphic encryption exceeding a threshold value, converting the encryption into a polynomial.   
     
     
         10 . The method for processing a homomorphic encryption of  claim 7 ,
 wherein the performing a modulus operation comprises:   converting a modulus value of the homomorphic encryption, and performing a modulus operation for the homomorphic encryption converted into a polynomial with the modulus value before conversion.   
     
     
         11 . A method for processing a homomorphic encryption, the method comprising:
 receiving an input of a message;   converting the message into a polynomial; and   generating a homomorphic encryption by using the message converted into a polynomial, a public key, and information for a public key encryption multiplier random polynomial,   wherein the public key encryption multiplier random polynomial is expressed as a polynomial having a plurality of terms, and   the information for the public key encryption multiplier random polynomial includes information on degrees and coefficients of the plurality of respective terms.   
     
     
         12 . The method for processing a homomorphic encryption of  claim 11 ,
 wherein the converting into a polynomial comprises:   using element values of the input message as they are as a plurality of coefficient values of the polynomial.   
     
     
         13 . The method for processing a homomorphic encryption of  claim 12 ,
 wherein the converting into a polynomial comprises:   based on the element values of the message not being integers, rounding off the values and converting the values into integers, and using the values converted into integers as the coefficient values of the polynomial.   
     
     
         14 . The method for processing a homomorphic encryption of  claim 11 ,
 wherein the public key was calculated by using information for a secret key including the information on the degrees and the coefficients of the plurality of respective terms.   
     
     
         15 . The method for processing a homomorphic encryption of  claim 14 ,
 wherein the secret key includes 64 terms, and   the coefficient information has a value of 1 or −1.   
     
     
         16 . The method for processing a homomorphic encryption of  claim 11 ,
 wherein the generating a homomorphic encryption comprises:   generating a homomorphic encryption expressed as a polynomial calculated by using only a last decimal q 0  from a predetermined ring.   
     
     
         17 . An operation device comprising:
 a memory storing at least one instruction; and   a processor executing the at least one instruction,   wherein the processor is configured to:   by executing the at least one instruction, performing decryption for a homomorphic encryption by using information for a secret key, and   the secret key is expressed as a polynomial having a plurality of terms, and   the information for the secret key includes information on degrees and coefficients of the plurality of respective terms.   
     
     
         18 . The operation device of  claim 17 ,
 wherein the secret key includes 64 terms, and   the coefficient information has a value of 1 or −1.   
     
     
         19 . The operation device of  claim 17 ,
 wherein the processor is configured to:   convert a homomorphic encryption into a polynomial having a plurality of respective slot values inside the homomorphic encryption as coefficient values,   modulus-operate the converted polynomial, and   convert the modulus-operated result into a homomorphic encryption having the plurality of respective coefficient values of the modulus-operated polynomial as slot values.   
     
     
         20 . The operation device of  claim 17 ,
 wherein the processor is configured to:   convert a message into a polynomial, and generate a homomorphic encryption by using the message converted into a polynomial, a public key, and information for a public key encryption multiplier random polynomial,   wherein the public key encryption multiplier random polynomial is expressed as a polynomial having a plurality of terms, and   the information for the public key encryption multiplier random polynomial includes information on degrees and coefficients of the plurality of respective terms.